type interval = BOT | INT of (int * int);;
let less x y = match x,y with
| BOT, _ -> true
| _, BOT -> false
| INT (a,b), INT (c,d) -> (a<=c)&&(b<=d);;
let join x y = match x,y with
| BOT, _ -> y
| _, BOT -> x
| INT (a,b), INT (c,d) -> INT (min a c,max b d);;
let meet x y = match x,y with
| BOT, _ -> BOT
| _, BOT -> BOT
| INT (a,b), INT (c,d) -> 
    if (b<c) or (d<a) then BOT
    else INT (max a c,min b d);;
let f (x0,x1,x2,x3,x4) =
  (INT (min_int,max_int),
   join (INT (1,1)) x3,
   meet x1 (INT (min_int,max_int)),
   (match x2 with
    | BOT -> BOT
    | INT (a,b) ->
        let a' = if a<max_int then a+1 else max_int in
          let b' = if b<max_int then b+1 else max_int in
            INT (a',b')),
   meet x1 BOT);;
let pless (x0,x1,x2,x3,x4) (x'0,x'1,x'2,x'3,x'4) =
 (less x0 x'0) && (less x1 x'1) && (less x2 x'2) && (less x3 x'3)
  && (less x4 x'4);;
let lfp leq a f = 
  let rec iterate x =
    let y = f x in
      if leq y x then x
      else iterate y
  in iterate a;;
lfp pless (BOT,BOT,BOT,BOT,BOT) f;;